Introduction to Elliptic Curves and Modular Forms

Neal Koblitz (auth.)0387960295, 9780387960296

The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book starts out with a problem from elementary number theory and proceeds to lead its reader into the modern theory, covering such topics as the Hasse-Weil L-function and the conjecture of Birch and Swinnerton-Dyer. The second edition of this text includes an updated bibliography indicating the latest, dramatic changes in the direction of proving the Birch and Swinnerton conjecture. It also discusses the current state of knowledge of elliptic curves.

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Table of contents :
Front Matter….Pages i-viii
From Congruent Numbers to Elliptic Curves….Pages 1-50
The Hasse—Weil L -Function of an Elliptic Curve….Pages 51-97
Modular Forms….Pages 98-175
Modular Forms of Half Integer Weight….Pages 176-222
Back Matter….Pages 223-250